The idea behind the Simple Moving Average (SMA) is to take the average of the last few observations and use it as a forecast for the next several steps ahead. Very crude and very simple. In fact, it has Naive (from this post) as a special case if you take the average of one most recent observation. On the other hand, if you increase the order to include all the observations, you will end up with the Global Mean. And this simple method works quite well if you have level data, i.e. no apparent strong trend, no obvious seasonality, and no other important elements of structure.

The only thing that makes it a bit harder to use in practice is the choice of the order, i.e. the number of observations to average over. Unfortunately, there is no universal answer here. But people report that the order of 12 or 13 is fine for weekly data, although it’s not completely clear why. In the academic literature, Aris Syntetos & John Boylan (2005) found that SMA(13) performed quite well on intermittent demand data, which was unexpected given the nature of the data (lots of zeroes). And almost 10 years ago, Fotios Petropoulos and I proposed a model underlying SMA with automatic order selection. We showed that it outperforms other simple benchmarks on supply chain data.

There is also some evidence from the VN2 inventory competition by Nicolas Vandeput. The benchmark there was built around a 13-week moving average with a simple seasonal adjustment, and only 25 out of 180+ participants managed to beat it. Many sophisticated ML pipelines lost to a method that predates computers.

So, if you work, for example, in retail or in supply chain, SMA is a method to consider for your sanity-check pool of models. But don’t expect miracles from it! It is still a simple method that works for level time series. Use it as a stepping stone to find a better model that has more features.

Anyone else found SMA to be a strong contender? Leave a comment – it would be interesting to see how many of you have had the same experience.

And yes, we discuss it in our “Demand Forecasting Principles” training in more detail. The next one will be held online in November, with live sessions from 2pm to 4pm UK time. We still have a few places left, so register here.

Message The Menace of ML: Simple Moving Average first appeared on OpenForecast.

First things first, SMA is simply the arithmetic mean of several recent observations. It has only one parameter: the number of observations used in the calculation (aka the “length”). For example, for SMA(13), we just take the last 13 observations, calculate the average, and use it as the point forecast for the next few observations. As simple as that!

SMA sits between two other simple forecasting methods: Naïve, which only relies on the most recent observation, and the global average, which uses all observations. The Naïve method works well for “Random walk” time series, which can be seen in finance, but not often in supply chain context. The global average is suitable for the series with the fixed level (“global level”), which are also rare in supply chain. Reality is usually somewhere in the middle. We know that average sales might go up or down gradually, but sudden jumps are uncommon in supply chain unless driven by some internal or external events. Also, supply chain data is typically not fast-moving and is often intermittent. In this situation, SMA does well.

The main challenge with SMA is in choosing the appropriate length. Petropoulos & Svetunkov (2017) showed that SMA has an underlying statistical model and demonstrated that the length can be selected for each time series based on information criteria. In practice, using an arbitrary length (e.g., 7, 12, or 13) often works fine too (see Sani & Kingsman, 1997, and Syntetos & Boylan, 2006) and can be used as a standard benchmark.

You might argue that SMA lacks important features, so it can’t be that good. Yes and no. While we can do better than SMA by accounting for seasonality, promotions, prices, etc., a more complex model might overfit and yield less accurate forecasts than SMA.

Take, for example, a recently finished VN1 competition of Nicolas Vandeput, where the winning Machine Learning approach improved upon SMA by about 40%. Still, out of 59 submissions, 10 failed to outperform SMA. This highlights two points:

1. you can achieve much better results than SMA with ML if you know what you’re doing;
2. SMA should be one of the standard benchmarks to make sure that your fancy approach outperforms it.

We’ll cover this and other aspects of forecasting methods in the “Demand Forecasting with R” course with Kandrika Pritularga next week. There are only a few places left, so act fast! Registration closes on the 4th, and the course starts on the 5th November (remember, remember the 5th of November!).

Message Why is it hard to beat the Simple Moving Average? first appeared on OpenForecast.

Abstract

Simple moving average (SMA) is a well-known forecasting method. It is easy to understand and interpret and easy to use, but it does not have an appropriate length selection mechanism and does not have an underlying statistical model. In this paper we show two statistical models underlying SMA and demonstrate that the automatic selection of the optimal length of the model can easily be done using this finding. We then evaluate the proposed model on a real dataset and compare its performance with other popular simple forecasting methods. We find that SMA performs better both in terms of point forecasts and prediction intervals in cases of normal and cumulative values.

Download the paper.
DOI.

Message Old dog, new tricks: a modelling view of simple moving averages first appeared on OpenForecast.